MinT - Best Known (257−166, 257, s)-Nets in Base 4

Best Known (257−166, 257, s)-Nets in Base 4

(257−166, 257, 104)-Net over F₄ — Constructive and digital

Digital (91, 257, 104)-net over F₄, using

t-expansion [i] based on digital (73, 257, 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]

(257−166, 257, 144)-Net over F₄ — Digital

Digital (91, 257, 144)-net over F₄, using

net from sequence [i] based on digital (91, 143)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 91 and N(F) ≥ 144, using
  - Drinfeld modules of rank 1 [i]

(257−166, 257, 706)-Net in Base 4 — Upper bound on s

There is no (91, 257, 707)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 55539 481270 610870 718808 462176 156023 817286 911760 776812 454956 702469 054200 671973 622352 128085 134734 330696 069464 892041 927607 556372 046541 002280 875529 791557 191392 > 4²⁵⁷ [i]