MinT - Best Known (151, 151+57, s)-Nets in Base 3

Best Known (151, 151+57, s)-Nets in Base 3

(151, 151+57, 288)-Net over F₃ — Constructive and digital

Digital (151, 208, 288)-net over F₃, using

2 times m-reduction [i] based on digital (151, 210, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 70, 96)-net over F₂₇, using
  - net from sequence [i] based on digital (11, 95)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96, using
      - an explicitly constructive algebraic function field [i]

(151, 151+57, 622)-Net over F₃ — Digital

Digital (151, 208, 622)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(151, 151+57, 18994)-Net in Base 3 — Upper bound on s

There is no (151, 208, 18995)-net in base 3, because

1 times m-reduction [i] would yield (151, 207, 18995)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 581 006564 258396 015654 761030 867142 006508 148004 216127 808148 337307 677268 235185 528074 350715 631827 802921 > 3²⁰⁷ [i]