MinT - Best Known (179−69, 179, s)-Nets in Base 4

Best Known (179−69, 179, s)-Nets in Base 4

(179−69, 179, 130)-Net over F₄ — Constructive and digital

Digital (110, 179, 130)-net over F₄, using

t-expansion [i] based on digital (105, 179, 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]

(179−69, 179, 301)-Net over F₄ — Digital

Digital (110, 179, 301)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(179−69, 179, 6374)-Net in Base 4 — Upper bound on s

There is no (110, 179, 6375)-net in base 4, because

1 times m-reduction [i] would yield (110, 178, 6375)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 147402 846709 515519 301420 297529 218395 399560 126673 747087 016283 114792 940165 700653 743372 298846 850128 330618 428341 > 4¹⁷⁸ [i]