MinT - Best Known (180−84, 180, s)-Nets in Base 4

Best Known (180−84, 180, s)-Nets in Base 4

(180−84, 180, 130)-Net over F₄ — Constructive and digital

Digital (96, 180, 130)-net over F₄, using

trace code for nets [i] based on digital (6, 90, 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]

(180−84, 180, 163)-Net over F₄ — Digital

Digital (96, 180, 163)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(180−84, 180, 2059)-Net in Base 4 — Upper bound on s

There is no (96, 180, 2060)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 370880 225918 465590 754913 251222 317657 678904 939602 778494 818270 303023 940394 738377 732193 919497 016500 129738 195520 > 4¹⁸⁰ [i]