MinT - Best Known (89, 89+104, s)-Nets in Base 4

Best Known (89, 89+104, s)-Nets in Base 4

(89, 89+104, 104)-Net over F₄ — Constructive and digital

Digital (89, 193, 104)-net over F₄, using

t-expansion [i] based on digital (73, 193, 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]

(89, 89+104, 129)-Net over F₄ — Digital

Digital (89, 193, 129)-net over F₄, using

t-expansion [i] based on digital (81, 193, 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]

(89, 89+104, 1114)-Net in Base 4 — Upper bound on s

There is no (89, 193, 1115)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 159 091667 611841 912470 894169 702565 062268 972553 063747 251330 256312 230412 653921 850884 979848 525377 014673 250074 063566 428076 > 4¹⁹³ [i]