MinT - Best Known (32, 32+36, s)-Nets in Base 128

Best Known (32, 32+36, s)-Nets in Base 128

(32, 32+36, 504)-Net over F₁₂₈ — Constructive and digital

Digital (32, 68, 504)-net over F₁₂₈, using

(u,Â u+v)-construction [i] based on
1. digital (5, 23, 216)-net over F₁₂₈, using
  - net from sequence [i] based on digital (5, 215)-sequence over F₁₂₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 5 and N(F) ≥ 216, using
      - a function field by SÃ©mirat [i]
2. digital (9, 45, 288)-net over F₁₂₈, using
  - net from sequence [i] based on digital (9, 287)-sequence over F₁₂₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 9 and N(F) ≥ 288, using
      - a function field by SÃ©mirat [i]

(32, 32+36, 547)-Net in Base 128 — Constructive

(32, 68, 547)-net in base 128, using

(u,Â u+v)-construction [i] based on
1. (5, 23, 259)-net in base 128, using
  - 1 times m-reduction [i] based on (5, 24, 259)-net in base 128, using
    - base change [i] based on digital (2, 21, 259)-net over F₂₅₆, using
      - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
        Niederreiter sequence [i]
2. digital (9, 45, 288)-net over F₁₂₈, using
  - net from sequence [i] based on digital (9, 287)-sequence over F₁₂₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 9 and N(F) ≥ 288, using
      - a function field by SÃ©mirat [i]

(32, 32+36, 1377)-Net over F₁₂₈ — Digital

Digital (32, 68, 1377)-net over F₁₂₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(32, 32+36, 5431210)-Net in Base 128 — Upper bound on s

There is no (32, 68, 5431211)-net in base 128, because

the generalized Rao bound for nets shows that 128^mÂ â‰¥ 195109 560151 114244 023094 215853 442236 253291 567709 938130 901838 727325 238893 749762 649513 702705 649692 486071 369393 259802 949910 544362 761395 094032 252562 > 128⁶⁸ [i]