MinT - Best Known (84, 84+71, s)-Nets in Base 4

Best Known (84, 84+71, s)-Nets in Base 4

(84, 84+71, 130)-Net over F₄ — Constructive and digital

Digital (84, 155, 130)-net over F₄, using

1 times m-reduction [i] based on digital (84, 156, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 78, 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]

(84, 84+71, 152)-Net over F₄ — Digital

Digital (84, 155, 152)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(84, 84+71, 2037)-Net in Base 4 — Upper bound on s

There is no (84, 155, 2038)-net in base 4, because

1 times m-reduction [i] would yield (84, 154, 2038)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 522 831780 719836 058863 191621 397287 995777 354598 666498 188621 518353 418869 098354 659189 671392 975926 > 4¹⁵⁴ [i]