MinT - Best Known (243−77, 243, s)-Nets in Base 3

Best Known (243−77, 243, s)-Nets in Base 3

(243−77, 243, 192)-Net over F₃ — Constructive and digital

Digital (166, 243, 192)-net over F₃, using

trace code for nets [i] based on digital (4, 81, 64)-net over F₂₇, using
- net from sequence [i] based on digital (4, 63)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 4 and N(F) ≥ 64, using
    - a function field by SÃ©mirat [i]

(243−77, 243, 442)-Net over F₃ — Digital

Digital (166, 243, 442)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(243−77, 243, 8171)-Net in Base 3 — Upper bound on s

There is no (166, 243, 8172)-net in base 3, because

1 times m-reduction [i] would yield (166, 242, 8172)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 29 141424 863681 434538 261815 732889 006807 643232 443667 674385 385653 280661 895387 093409 746848 148299 847515 799049 440898 382665 > 3²⁴² [i]