MinT - Best Known (176−82, 176, s)-Nets in Base 4

Best Known (176−82, 176, s)-Nets in Base 4

(176−82, 176, 130)-Net over F₄ — Constructive and digital

Digital (94, 176, 130)-net over F₄, using

trace code for nets [i] based on digital (6, 88, 65)-net over F₁₆, using
- net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
    - the Hermitian function field over F₁₆ [i]

(176−82, 176, 160)-Net over F₄ — Digital

Digital (94, 176, 160)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(176−82, 176, 2033)-Net in Base 4 — Upper bound on s

There is no (94, 176, 2034)-net in base 4, because

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]