MinT - Best Known (100, 100+93, s)-Nets in Base 3

Best Known (100, 100+93, s)-Nets in Base 3

(100, 100+93, 74)-Net over F₃ — Constructive and digital

Digital (100, 193, 74)-net over F₃, using

(u,Â u+v)-construction [i] based on
1. digital (27, 73, 37)-net over F₃, using
  - net from sequence [i] based on digital (27, 36)-sequence over F₃, using
    - Niederreiterâ€“Xing sequence constructionÂ III based on the algebraic function field F/F₃ with g(F)Â =Â 26, N(F)Â =Â 36, and 1 place with degree 2 [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 (27, 120, 37)-net over F₃, using
  - net from sequence [i] based on digital (27, 36)-sequence over F₃ (see above)

(100, 100+93, 108)-Net over F₃ — Digital

Digital (100, 193, 108)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(100, 100+93, 837)-Net in Base 3 — Upper bound on s

There is no (100, 193, 838)-net in base 3, because

1 times m-reduction [i] would yield (100, 192, 838)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 40 811538 969339 317764 619527 977829 677058 537180 893649 653020 397082 241984 349948 888928 695232 952997 > 3¹⁹² [i]