MinT - Best Known (99, 99+83, s)-Nets in Base 3

Best Known (99, 99+83, s)-Nets in Base 3

(99, 99+83, 80)-Net over F₃ — Constructive and digital

Digital (99, 182, 80)-net over F₃, using

trace code for nets [i] based on digital (8, 91, 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]

(99, 99+83, 119)-Net over F₃ — Digital

Digital (99, 182, 119)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(99, 99+83, 991)-Net in Base 3 — Upper bound on s

There is no (99, 182, 992)-net in base 3, because

1 times m-reduction [i] would yield (99, 181, 992)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 237 733656 103037 865032 400888 208042 882632 440196 260034 138218 074940 225374 666466 179647 671745 > 3¹⁸¹ [i]