MinT - Best Known (11, 11+58, s)-Nets in Base 27

Best Known (11, 11+58, s)-Nets in Base 27

(11, 11+58, 96)-Net over F₂₇ — Constructive and digital

Digital (11, 69, 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]

(11, 11+58, 100)-Net over F₂₇ — Digital

Digital (11, 69, 100)-net over F₂₇, using

net from sequence [i] based on digital (11, 99)-sequence over F₂₇, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 100, using
  - a curve from the manYPoints database [i]

(11, 11+58, 1127)-Net in Base 27 — Upper bound on s

There is no (11, 69, 1128)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 591 300078 851384 379298 461140 094168 142698 433059 486766 672035 318499 021218 334803 131845 316973 368390 316433 > 27⁶⁹ [i]