MinT - Best Known (157−90, 157, s)-Nets in Base 3

Best Known (157−90, 157, s)-Nets in Base 3

(157−90, 157, 48)-Net over F₃ — Constructive and digital

Digital (67, 157, 48)-net over F₃, using

t-expansion [i] based on digital (45, 157, 48)-net over F₃, using
- net from sequence [i] based on digital (45, 47)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 45 and N(F) ≥ 48, using
    - an explicitly constructive algebraic function field [i]

(157−90, 157, 72)-Net over F₃ — Digital

Digital (67, 157, 72)-net over F₃, using

net from sequence [i] based on digital (67, 71)-sequence over F₃, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 67 and N(F) ≥ 72, using
  - algebraic function fields over â„¤₃ by Niederreiter/Xing [i]

(157−90, 157, 364)-Net in Base 3 — Upper bound on s

There is no (67, 157, 365)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 848 134363 680974 801022 009978 092154 654784 597603 859525 605877 085136 352133 754059 > 3¹⁵⁷ [i]