MinT - Best Known (242−114, 242, s)-Nets in Base 3

Best Known (242−114, 242, s)-Nets in Base 3

(242−114, 242, 84)-Net over F₃ — Constructive and digital

Digital (128, 242, 84)-net over F₃, using

(u,Â u+v)-construction [i] based on
1. digital (26, 83, 36)-net over F₃, using
  - net from sequence [i] based on digital (26, 35)-sequence over F₃, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 26 and N(F) ≥ 36, using
      - an explicitly constructive algebraic function field [i]
2. digital (45, 159, 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]

(242−114, 242, 140)-Net over F₃ — Digital

Digital (128, 242, 140)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(242−114, 242, 1115)-Net in Base 3 — Upper bound on s

There is no (128, 242, 1116)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 29 310189 617968 969093 934558 160231 627434 849671 862590 859966 649179 008388 598421 736002 177805 936982 034935 749417 389957 306681 > 3²⁴² [i]