MinT - Best Known (117−47, 117, s)-Nets in Base 4

Best Known (117−47, 117, s)-Nets in Base 4

(117−47, 117, 130)-Net over F₄ — Constructive and digital

Digital (70, 117, 130)-net over F₄, using

11 times m-reduction [i] based on digital (70, 128, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 64, 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]

(117−47, 117, 184)-Net over F₄ — Digital

Digital (70, 117, 184)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(117−47, 117, 3399)-Net in Base 4 — Upper bound on s

There is no (70, 117, 3400)-net in base 4, because

1 times m-reduction [i] would yield (70, 116, 3400)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 6916 482305 940272 372592 683818 775612 266637 985611 091861 827340 685424 848996 > 4¹¹⁶ [i]