MinT - Best Known (153−43, 153, s)-Nets in Base 3

Best Known (153−43, 153, s)-Nets in Base 3

(153−43, 153, 252)-Net over F₃ — Constructive and digital

Digital (110, 153, 252)-net over F₃, using

trace code for nets [i] based on digital (8, 51, 84)-net over F₂₇, using
- net from sequence [i] based on digital (8, 83)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 8 and N(F) ≥ 84, using
    - a function field by SÃ©mirat [i]

(153−43, 153, 441)-Net over F₃ — Digital

Digital (110, 153, 441)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(153−43, 153, 12308)-Net in Base 3 — Upper bound on s

There is no (110, 153, 12309)-net in base 3, because

1 times m-reduction [i] would yield (110, 152, 12309)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3 335264 045917 762731 891585 561100 585857 097996 025775 847636 629528 668767 744763 > 3¹⁵² [i]