MinT - Best Known (81, 81+156, s)-Nets in Base 4

Best Known (81, 81+156, s)-Nets in Base 4

(81, 81+156, 104)-Net over F₄ — Constructive and digital

Digital (81, 237, 104)-net over F₄, using

t-expansion [i] based on digital (73, 237, 104)-net over F₄, using
- net from sequence [i] based on digital (73, 103)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
    - F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(81, 81+156, 129)-Net over F₄ — Digital

Digital (81, 237, 129)-net over F₄, using

net from sequence [i] based on digital (81, 128)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 81 and N(F) ≥ 129, using
  - Drinfeld modules of rank 1 [i]

(81, 81+156, 609)-Net in Base 4 — Upper bound on s

There is no (81, 237, 610)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 51161 366763 786788 748530 077581 539403 895441 042386 604256 038833 233886 668716 241357 743796 219400 532767 578997 363919 146111 862485 087646 886894 865877 727056 > 4²³⁷ [i]