MinT - Best Known (4, 55, s)-Nets in Base 128

Best Known (4, 55, s)-Nets in Base 128

(4, 55, 192)-Net over F₁₂₈ — Constructive and digital

Digital (4, 55, 192)-net over F₁₂₈, using

t-expansion [i] based on digital (3, 55, 192)-net over F₁₂₈, using
- net from sequence [i] based on digital (3, 191)-sequence over F₁₂₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 3 and N(F) ≥ 192, using
    - a function field by SÃ©mirat [i]

(4, 55, 215)-Net over F₁₂₈ — Digital

Digital (4, 55, 215)-net over F₁₂₈, using

net from sequence [i] based on digital (4, 214)-sequence over F₁₂₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 4 and N(F) ≥ 215, using
  - a curve from the manYPoints database [i]

(4, 55, 2811)-Net in Base 128 — Upper bound on s

There is no (4, 55, 2812)-net in base 128, because

7 times m-reduction [i] would yield (4, 48, 2812)-net in base 128, but
- the generalized Rao bound for nets shows that 128^mÂ â‰¥ 140417 822584 071944 770460 154931 018936 977601 663247 674921 957406 554173 074207 475708 863843 188087 852394 403654 > 128⁴⁸ [i]