MinT - Best Known (91, 91+164, s)-Nets in Base 4

Best Known (91, 91+164, s)-Nets in Base 4

(91, 91+164, 104)-Net over F₄ — Constructive and digital

Digital (91, 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]

(91, 91+164, 144)-Net over F₄ — Digital

Digital (91, 255, 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]

(91, 91+164, 712)-Net in Base 4 — Upper bound on s

There is no (91, 255, 713)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3453 510376 306847 767431 434281 088188 364145 575814 355174 750788 310398 002705 989571 945813 574912 630157 941577 603632 756245 971553 104399 788769 181065 218533 085070 678240 > 4²⁵⁵ [i]