MinT - Best Known (22, 46, s)-Nets in Base 128

Best Known (22, 46, s)-Nets in Base 128

(22, 46, 438)-Net over F₁₂₈ — Constructive and digital

Digital (22, 46, 438)-net over F₁₂₈, using

(u,Â u+v)-construction [i] based on
1. digital (1, 13, 150)-net over F₁₂₈, using
  - net from sequence [i] based on digital (1, 149)-sequence over F₁₂₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 1 and N(F) ≥ 150, using
      - a function field by SÃ©mirat [i]
2. digital (9, 33, 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]

(22, 46, 518)-Net in Base 128 — Constructive

(22, 46, 518)-net in base 128, using

(u,Â u+v)-construction [i] based on
1. (4, 16, 259)-net in base 128, using
  - base change [i] based on digital (2, 14, 259)-net over F₂₅₆, using
    - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
      - Niederreiter sequence [i]
2. (6, 30, 259)-net in base 128, using
  - 2 times m-reduction [i] based on (6, 32, 259)-net in base 128, using
    - base change [i] based on digital (2, 28, 259)-net over F₂₅₆, using
      - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆ (see above)

(22, 46, 1228)-Net over F₁₂₈ — Digital

Digital (22, 46, 1228)-net over F₁₂₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(22, 46, 4979611)-Net in Base 128 — Upper bound on s

There is no (22, 46, 4979612)-net in base 128, because

the generalized Rao bound for nets shows that 128^mÂ â‰¥ 8 543967 752927 315197 181654 955075 602564 017083 149203 859371 545884 504362 875880 258162 597177 670700 281812 > 128⁴⁶ [i]