MinT - Best Known (12, 12+73, s)-Nets in Base 27

Best Known (12, 12+73, s)-Nets in Base 27

(12, 12+73, 96)-Net over F₂₇ — Constructive and digital

Digital (12, 85, 96)-net over F₂₇, using

t-expansion [i] based on digital (11, 85, 96)-net over F₂₇, using
- net from sequence [i] based on digital (11, 95)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96, using
    - an explicitly constructive algebraic function field [i]

(12, 12+73, 109)-Net over F₂₇ — Digital

Digital (12, 85, 109)-net over F₂₇, using

net from sequence [i] based on digital (12, 108)-sequence over F₂₇, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 12 and N(F) ≥ 109, using
  - a curve from the manYPoints database [i]

(12, 12+73, 1182)-Net in Base 27 — Upper bound on s

There is no (12, 85, 1183)-net in base 27, because

1 times m-reduction [i] would yield (12, 84, 1183)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 1 748685 134915 519143 879412 509990 902440 443414 372487 036374 933012 213069 216692 098098 459318 974264 897948 782112 300118 022388 179033 > 27⁸⁴ [i]