MinT - Best Known (148−58, 148, s)-Nets in Base 4

Best Known (148−58, 148, s)-Nets in Base 4

(148−58, 148, 130)-Net over F₄ — Constructive and digital

Digital (90, 148, 130)-net over F₄, using

20 times m-reduction [i] based on digital (90, 168, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 84, 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]

(148−58, 148, 242)-Net over F₄ — Digital

Digital (90, 148, 242)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(148−58, 148, 4574)-Net in Base 4 — Upper bound on s

There is no (90, 148, 4575)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 127695 503203 488832 732362 637906 017292 911868 868992 492283 165477 775860 739527 661012 590060 686270 > 4¹⁴⁸ [i]