MinT - Best Known (207−60, 207, s)-Nets in Base 3

Best Known (207−60, 207, s)-Nets in Base 3

(207−60, 207, 264)-Net over F₃ — Constructive and digital

Digital (147, 207, 264)-net over F₃, using

trace code for nets [i] based on digital (9, 69, 88)-net over F₂₇, using
- net from sequence [i] based on digital (9, 87)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 9 and N(F) ≥ 88, using
    - a function field by SÃ©mirat [i]

(207−60, 207, 511)-Net over F₃ — Digital

Digital (147, 207, 511)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(207−60, 207, 11770)-Net in Base 3 — Upper bound on s

There is no (147, 207, 11771)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 581 056133 795438 971604 135750 692184 026776 894218 885628 083390 681761 352070 734810 855344 928783 611409 570013 > 3²⁰⁷ [i]