MinT - Best Known (88, 226, s)-Nets in Base 4

Best Known (88, 226, s)-Nets in Base 4

(88, 226, 104)-Net over F₄ — Constructive and digital

Digital (88, 226, 104)-net over F₄, using

t-expansion [i] based on digital (73, 226, 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]

(88, 226, 129)-Net over F₄ — Digital

Digital (88, 226, 129)-net over F₄, using

t-expansion [i] based on digital (81, 226, 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]

(88, 226, 773)-Net in Base 4 — Upper bound on s

There is no (88, 226, 774)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 12258 778524 707571 465282 814967 186065 932827 296226 691199 918987 842864 992216 963231 258662 173242 826991 473386 582834 063605 398684 187261 816695 256204 > 4²²⁶ [i]