MinT - Best Known (100, 100+83, s)-Nets in Base 4

Best Known (100, 100+83, s)-Nets in Base 4

(100, 100+83, 130)-Net over F₄ — Constructive and digital

Digital (100, 183, 130)-net over F₄, using

5 times m-reduction [i] based on digital (100, 188, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 94, 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]

(100, 100+83, 181)-Net over F₄ — Digital

Digital (100, 183, 181)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(100, 100+83, 2497)-Net in Base 4 — Upper bound on s

There is no (100, 183, 2498)-net in base 4, because

1 times m-reduction [i] would yield (100, 182, 2498)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 37 671374 576855 452361 015048 923532 060771 251233 545238 264878 066492 186697 366635 856939 780428 635590 654856 771303 230760 > 4¹⁸² [i]