MinT - Best Known (118, 118+109, s)-Nets in Base 3

Best Known (118, 118+109, s)-Nets in Base 3

(118, 118+109, 76)-Net over F₃ — Constructive and digital

Digital (118, 227, 76)-net over F₃, using

(u,Â u+v)-construction [i] based on
1. digital (32, 86, 38)-net over F₃, using
  - net from sequence [i] based on digital (32, 37)-sequence over F₃, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 32 and N(F) ≥ 38, using
      - an explicitly constructive algebraic function field [i]
2. digital (32, 141, 38)-net over F₃, using
  - net from sequence [i] based on digital (32, 37)-sequence over F₃ (see above)

(118, 118+109, 125)-Net over F₃ — Digital

Digital (118, 227, 125)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(118, 118+109, 988)-Net in Base 3 — Upper bound on s

There is no (118, 227, 989)-net in base 3, because

1 times m-reduction [i] would yield (118, 226, 989)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 697143 838208 897447 177234 271357 943723 999862 786858 510687 347203 327414 814047 323335 043348 732199 634568 023851 209073 > 3²²⁶ [i]