MinT - Best Known (157, 157+71, s)-Nets in Base 3

Best Known (157, 157+71, s)-Nets in Base 3

(157, 157+71, 204)-Net over F₃ — Constructive and digital

Digital (157, 228, 204)-net over F₃, using

trace code for nets [i] based on digital (5, 76, 68)-net over F₂₇, using
- net from sequence [i] based on digital (5, 67)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 5 and N(F) ≥ 68, using
    - a function field by SÃ©mirat [i]

(157, 157+71, 442)-Net over F₃ — Digital

Digital (157, 228, 442)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(157, 157+71, 8609)-Net in Base 3 — Upper bound on s

There is no (157, 228, 8610)-net in base 3, because

1 times m-reduction [i] would yield (157, 227, 8610)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2 030542 274351 651286 951933 773575 848556 321148 902619 084613 644878 792424 076949 761310 446609 235590 874345 825348 384401 > 3²²⁷ [i]