MinT - Best Known (226−118, 226, s)-Nets in Base 4

Best Known (226−118, 226, s)-Nets in Base 4

(226−118, 226, 130)-Net over F₄ — Constructive and digital

Digital (108, 226, 130)-net over F₄, using

t-expansion [i] based on digital (105, 226, 130)-net over F₄, using
- net from sequence [i] based on digital (105, 129)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 105 and N(F) ≥ 130, using
    - T₇ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(226−118, 226, 144)-Net over F₄ — Digital

Digital (108, 226, 144)-net over F₄, using

t-expansion [i] based on digital (91, 226, 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]

(226−118, 226, 1491)-Net in Base 4 — Upper bound on s

There is no (108, 226, 1492)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 11839 330402 659847 416293 001071 988444 493778 995304 726759 694870 218573 169539 985495 189893 586477 573500 887332 379547 560930 325026 530044 548767 131752 > 4²²⁶ [i]