MinT - Best Known (229−105, 229, s)-Nets in Base 4

Best Known (229−105, 229, s)-Nets in Base 4

(229−105, 229, 130)-Net over F₄ — Constructive and digital

Digital (124, 229, 130)-net over F₄, using

t-expansion [i] based on digital (105, 229, 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]

(229−105, 229, 213)-Net over F₄ — Digital

Digital (124, 229, 213)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(229−105, 229, 2898)-Net in Base 4 — Upper bound on s

There is no (124, 229, 2899)-net in base 4, because

1 times m-reduction [i] would yield (124, 228, 2899)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 186199 528462 870076 389471 319329 002585 815123 117470 769413 318832 995855 273802 032421 702210 638930 219809 337340 442783 846211 785027 318602 066999 349520 > 4²²⁸ [i]