MinT - Best Known (99, 99+61, s)-Nets in Base 4

Best Known (99, 99+61, s)-Nets in Base 4

(99, 99+61, 130)-Net over F₄ — Constructive and digital

Digital (99, 160, 130)-net over F₄, using

26 times m-reduction [i] based on digital (99, 186, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 93, 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]

(99, 99+61, 284)-Net over F₄ — Digital

Digital (99, 160, 284)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(99, 99+61, 6206)-Net in Base 4 — Upper bound on s

There is no (99, 160, 6207)-net in base 4, because

1 times m-reduction [i] would yield (99, 159, 6207)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 534168 498085 359333 704019 817633 172439 899816 815328 831479 478333 706383 486333 911350 664554 725613 972331 > 4¹⁵⁹ [i]