MinT - Best Known (177−83, 177, s)-Nets in Base 4

Best Known (177−83, 177, s)-Nets in Base 4

(177−83, 177, 104)-Net over F₄ — Constructive and digital

Digital (94, 177, 104)-net over F₄, using

t-expansion [i] based on digital (73, 177, 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]

(177−83, 177, 158)-Net over F₄ — Digital

Digital (94, 177, 158)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(177−83, 177, 2033)-Net in Base 4 — Upper bound on s

There is no (94, 177, 2034)-net in base 4, because

1 times m-reduction [i] would yield (94, 176, 2034)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 9342 219520 176687 081866 757272 766815 352734 528860 088522 025086 547967 164828 642856 759147 856232 319904 850796 111138 > 4¹⁷⁶ [i]