MinT - Best Known (216−61, 216, s)-Nets in Base 3

Best Known (216−61, 216, s)-Nets in Base 3

(216−61, 216, 288)-Net over F₃ — Constructive and digital

Digital (155, 216, 288)-net over F₃, using

trace code for nets [i] based on digital (11, 72, 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]

(216−61, 216, 578)-Net over F₃ — Digital

Digital (155, 216, 578)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(216−61, 216, 15787)-Net in Base 3 — Upper bound on s

There is no (155, 216, 15788)-net in base 3, because

1 times m-reduction [i] would yield (155, 215, 15788)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3 813784 670453 046280 708884 606150 574273 442333 855716 254306 075071 930649 952060 409652 521703 576912 504232 942665 > 3²¹⁵ [i]