MinT - Best Known (182−78, 182, s)-Nets in Base 4

Best Known (182−78, 182, s)-Nets in Base 4

(182−78, 182, 130)-Net over F₄ — Constructive and digital

Digital (104, 182, 130)-net over F₄, using

14 times m-reduction [i] based on digital (104, 196, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 98, 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]

(182−78, 182, 216)-Net over F₄ — Digital

Digital (104, 182, 216)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(182−78, 182, 3278)-Net in Base 4 — Upper bound on s

There is no (104, 182, 3279)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 37 665898 491635 841953 782100 473228 084545 360414 361813 141757 296516 606930 913335 890744 954693 608959 550466 630227 078008 > 4¹⁸² [i]