MinT - Best Known (62, 62+43, s)-Nets in Base 4

Best Known (62, 62+43, s)-Nets in Base 4

(62, 62+43, 130)-Net over F₄ — Constructive and digital

Digital (62, 105, 130)-net over F₄, using

7 times m-reduction [i] based on digital (62, 112, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 56, 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]

(62, 62+43, 158)-Net over F₄ — Digital

Digital (62, 105, 158)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(62, 62+43, 2756)-Net in Base 4 — Upper bound on s

There is no (62, 105, 2757)-net in base 4, because

1 times m-reduction [i] would yield (62, 104, 2757)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 413 338727 061570 280688 564053 260170 283959 247770 987494 739373 240208 > 4¹⁰⁴ [i]