MinT - Best Known (113, 113+95, s)-Nets in Base 3

Best Known (113, 113+95, s)-Nets in Base 3

(113, 113+95, 80)-Net over F₃ — Constructive and digital

Digital (113, 208, 80)-net over F₃, using

2 times m-reduction [i] based on digital (113, 210, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 105, 40)-net over F₉, using
  - net from sequence [i] based on digital (8, 39)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
      - a function field by SÃ©mirat [i]

(113, 113+95, 133)-Net over F₃ — Digital

Digital (113, 208, 133)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(113, 113+95, 1114)-Net in Base 3 — Upper bound on s

There is no (113, 208, 1115)-net in base 3, because

1 times m-reduction [i] would yield (113, 207, 1115)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 600 175737 089212 140340 983497 542496 567901 866577 829604 255314 957576 152641 487168 824267 526820 275947 594259 > 3²⁰⁷ [i]