MinT - Best Known (227−107, 227, s)-Nets in Base 4

Best Known (227−107, 227, s)-Nets in Base 4

(227−107, 227, 130)-Net over F₄ — Constructive and digital

Digital (120, 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]

(227−107, 227, 194)-Net over F₄ — Digital

Digital (120, 227, 194)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(227−107, 227, 2491)-Net in Base 4 — Upper bound on s

There is no (120, 227, 2492)-net in base 4, because

1 times m-reduction [i] would yield (120, 226, 2492)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 11770 613468 599932 809583 632116 991834 986512 341138 607398 370324 153887 422997 057115 386039 254234 301187 734789 021506 667172 794638 377579 327898 963558 > 4²²⁶ [i]