MinT - Best Known (216−65, 216, s)-Nets in Base 3

Best Known (216−65, 216, s)-Nets in Base 3

(216−65, 216, 246)-Net over F₃ — Constructive and digital

Digital (151, 216, 246)-net over F₃, using

trace code for nets [i] based on digital (7, 72, 82)-net over F₂₇, using
- net from sequence [i] based on digital (7, 81)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 7 and N(F) ≥ 82, using
    - a function field by SÃ©mirat [i]

(216−65, 216, 469)-Net over F₃ — Digital

Digital (151, 216, 469)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(216−65, 216, 10237)-Net in Base 3 — Upper bound on s

There is no (151, 216, 10238)-net in base 3, because

1 times m-reduction [i] would yield (151, 215, 10238)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3 822180 101811 458076 823513 041961 549832 594777 381676 980594 221357 623927 117949 705534 377167 699442 827635 066689 > 3²¹⁵ [i]