MinT - Best Known (81, 81+174, s)-Nets in Base 4

Best Known (81, 81+174, s)-Nets in Base 4

(81, 81+174, 104)-Net over F₄ — Constructive and digital

Digital (81, 255, 104)-net over F₄, using

t-expansion [i] based on digital (73, 255, 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+174, 129)-Net over F₄ — Digital

Digital (81, 255, 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+174, 574)-Net in Base 4 — Upper bound on s

There is no (81, 255, 575)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3670 012958 468696 144530 961439 626699 026202 898058 724542 168898 161784 949612 168135 671783 436649 882125 932395 248794 990062 293310 411984 802851 323629 568963 694397 519200 > 4²⁵⁵ [i]