MinT - Best Known (183−84, 183, s)-Nets in Base 4

Best Known (183−84, 183, s)-Nets in Base 4

(183−84, 183, 130)-Net over F₄ — Constructive and digital

Digital (99, 183, 130)-net over F₄, using

3 times m-reduction [i] based on digital (99, 186, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 93, 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]

(183−84, 183, 174)-Net over F₄ — Digital

Digital (99, 183, 174)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(183−84, 183, 2277)-Net in Base 4 — Upper bound on s

There is no (99, 183, 2278)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 151 811263 040905 237054 819283 674058 377337 818653 970499 587218 029371 013032 784555 669267 856445 176663 502361 456721 469744 > 4¹⁸³ [i]