MinT - Best Known (181−81, 181, s)-Nets in Base 4

Best Known (181−81, 181, s)-Nets in Base 4

(181−81, 181, 130)-Net over F₄ — Constructive and digital

Digital (100, 181, 130)-net over F₄, using

7 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]

(181−81, 181, 187)-Net over F₄ — Digital

Digital (100, 181, 187)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(181−81, 181, 2658)-Net in Base 4 — Upper bound on s

There is no (100, 181, 2659)-net in base 4, because

1 times m-reduction [i] would yield (100, 180, 2659)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 366722 329029 797075 319529 683040 753898 335294 176777 243067 726451 458025 822859 225111 641709 393591 065007 024021 774536 > 4¹⁸⁰ [i]