MinT - Best Known (227−103, 227, s)-Nets in Base 4

Best Known (227−103, 227, s)-Nets in Base 4

(227−103, 227, 130)-Net over F₄ — Constructive and digital

Digital (124, 227, 130)-net over F₄, using

t-expansion [i] based on digital (105, 227, 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]

(227−103, 227, 218)-Net over F₄ — Digital

Digital (124, 227, 218)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(227−103, 227, 3039)-Net in Base 4 — Upper bound on s

There is no (124, 227, 3040)-net in base 4, because

1 times m-reduction [i] would yield (124, 226, 3040)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 11788 015381 656370 323254 976983 782630 498561 938296 756315 617098 794945 509483 015325 649402 619087 621244 703285 366725 013926 203111 257373 253691 063250 > 4²²⁶ [i]