MinT - Best Known (89, 89+79, s)-Nets in Base 4

Best Known (89, 89+79, s)-Nets in Base 4

(89, 89+79, 104)-Net over F₄ — Constructive and digital

Digital (89, 168, 104)-net over F₄, using

t-expansion [i] based on digital (73, 168, 104)-net over F₄, using
- net from sequence [i] based on digital (73, 103)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
    - F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(89, 89+79, 150)-Net over F₄ — Digital

Digital (89, 168, 150)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(89, 89+79, 1910)-Net in Base 4 — Upper bound on s

There is no (89, 168, 1911)-net in base 4, because

1 times m-reduction [i] would yield (89, 167, 1911)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 35223 825531 744771 298348 982736 994890 058236 639710 699413 830576 562886 166532 096990 276134 088540 643542 594396 > 4¹⁶⁷ [i]