MinT - Best Known (226−101, 226, s)-Nets in Base 4

Best Known (226−101, 226, s)-Nets in Base 4

(226−101, 226, 130)-Net over F₄ — Constructive and digital

Digital (125, 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]

(226−101, 226, 228)-Net over F₄ — Digital

Digital (125, 226, 228)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(226−101, 226, 3284)-Net in Base 4 — Upper bound on s

There is no (125, 226, 3285)-net in base 4, because

1 times m-reduction [i] would yield (125, 225, 3285)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2943 903593 806597 386343 540761 235599 721338 241639 936916 437949 622731 014926 211104 014772 534111 893147 083272 077744 806306 858340 965814 180578 004500 > 4²²⁵ [i]