MinT - Best Known (77−61, 77, s)-Nets in Base 27

Best Known (77−61, 77, s)-Nets in Base 27

(77−61, 77, 96)-Net over F₂₇ — Constructive and digital

Digital (16, 77, 96)-net over F₂₇, using

t-expansion [i] based on digital (11, 77, 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]

(77−61, 77, 144)-Net over F₂₇ — Digital

Digital (16, 77, 144)-net over F₂₇, using

net from sequence [i] based on digital (16, 143)-sequence over F₂₇, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 16 and N(F) ≥ 144, using
  - a curve from the manYPoints database [i]

(77−61, 77, 1942)-Net in Base 27 — Upper bound on s

There is no (16, 77, 1943)-net in base 27, because

1 times m-reduction [i] would yield (16, 76, 1943)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 6 082542 200146 643822 924990 166191 874322 363788 672985 404988 033305 514034 829502 663157 187817 952049 008147 739378 259045 > 27⁷⁶ [i]