MinT - Best Known (105, 226, s)-Nets in Base 4

Best Known (105, 226, s)-Nets in Base 4

(105, 226, 130)-Net over F₄ — Constructive and digital

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]

(105, 226, 144)-Net over F₄ — Digital

Digital (105, 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]

(105, 226, 1350)-Net in Base 4 — Upper bound on s

There is no (105, 226, 1351)-net in base 4, because

1 times m-reduction [i] would yield (105, 225, 1351)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2963 930439 035008 916289 421001 093263 765917 144608 870000 190921 317591 960183 724802 255675 764456 706557 233916 513670 561602 309082 490475 658825 824856 > 4²²⁵ [i]