MinT - Best Known (216−63, 216, s)-Nets in Base 3

Best Known (216−63, 216, s)-Nets in Base 3

(216−63, 216, 264)-Net over F₃ — Constructive and digital

Digital (153, 216, 264)-net over F₃, using

trace code for nets [i] based on digital (9, 72, 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]

(216−63, 216, 519)-Net over F₃ — Digital

Digital (153, 216, 519)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(216−63, 216, 12618)-Net in Base 3 — Upper bound on s

There is no (153, 216, 12619)-net in base 3, because

1 times m-reduction [i] would yield (153, 215, 12619)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3 811970 869195 538220 021185 987526 122096 576830 975444 954419 495375 426106 864589 464638 021056 683285 421284 301811 > 3²¹⁵ [i]