MinT - Best Known (182−79, 182, s)-Nets in Base 4

Best Known (182−79, 182, s)-Nets in Base 4

(182−79, 182, 130)-Net over F₄ — Constructive and digital

Digital (103, 182, 130)-net over F₄, using

12 times m-reduction [i] based on digital (103, 194, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 97, 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]

(182−79, 182, 207)-Net over F₄ — Digital

Digital (103, 182, 207)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(182−79, 182, 3163)-Net in Base 4 — Upper bound on s

There is no (103, 182, 3164)-net in base 4, because

1 times m-reduction [i] would yield (103, 181, 3164)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 9 487684 554512 394302 861335 438373 368290 941446 030084 266784 385258 770462 606896 909049 573481 749153 805894 278023 100804 > 4¹⁸¹ [i]