MinT - Best Known (104, 104+101, s)-Nets in Base 3

Best Known (104, 104+101, s)-Nets in Base 3

(104, 104+101, 74)-Net over F₃ — Constructive and digital

Digital (104, 205, 74)-net over F₃, using

(u,Â u+v)-construction [i] based on
1. digital (27, 77, 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, 128, 37)-net over F₃, using
  - net from sequence [i] based on digital (27, 36)-sequence over F₃ (see above)

(104, 104+101, 107)-Net over F₃ — Digital

Digital (104, 205, 107)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(104, 104+101, 813)-Net in Base 3 — Upper bound on s

There is no (104, 205, 814)-net in base 3, because

1 times m-reduction [i] would yield (104, 204, 814)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 22 523475 473441 412693 041703 931468 103030 130811 441383 562469 057872 903123 312313 374275 817507 989331 023357 > 3²⁰⁴ [i]