MinT - Best Known (48, 108, s)-Nets in Base 32

Best Known (48, 108, s)-Nets in Base 32

(48, 108, 218)-Net over F₃₂ — Constructive and digital

Digital (48, 108, 218)-net over F₃₂, using

(u,Â u+v)-construction [i] based on
1. digital (7, 37, 98)-net over F₃₂, using
  - net from sequence [i] based on digital (7, 97)-sequence over F₃₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 7 and N(F) ≥ 98, using
      - a function field by SÃ©mirat [i]
2. digital (11, 71, 120)-net over F₃₂, using
  - net from sequence [i] based on digital (11, 119)-sequence over F₃₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 11 and N(F) ≥ 120, using
      - a function field by SÃ©mirat [i]

(48, 108, 410)-Net over F₃₂ — Digital

Digital (48, 108, 410)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(48, 108, 513)-Net in Base 32 — Constructive

(48, 108, 513)-net in base 32, using

t-expansion [i] based on (46, 108, 513)-net in base 32, using
- base change [i] based on digital (28, 90, 513)-net over F₆₄, using
  - net from sequence [i] based on digital (28, 512)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513, using
      - the Hermitian function field over F₆₄ [i]

(48, 108, 101835)-Net in Base 32 — Upper bound on s

There is no (48, 108, 101836)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3 599228 588709 354432 958407 080027 693812 512754 969644 926786 682237 652800 722886 936714 144241 098470 150926 257343 601702 594036 926623 456665 370406 002340 661347 921345 490332 385680 > 32¹⁰⁸ [i]