MinT - Best Known (227−101, 227, s)-Nets in Base 4

Best Known (227−101, 227, s)-Nets in Base 4

(227−101, 227, 130)-Net over F₄ — Constructive and digital

Digital (126, 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]

(227−101, 227, 232)-Net over F₄ — Digital

Digital (126, 227, 232)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(227−101, 227, 3377)-Net in Base 4 — Upper bound on s

There is no (126, 227, 3378)-net in base 4, because

1 times m-reduction [i] would yield (126, 226, 3378)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 11689 728697 417989 762455 409293 286604 174804 435256 262580 607838 041193 376173 934951 334793 058589 583919 855182 563024 161092 285437 174986 722568 822696 > 4²²⁶ [i]