MinT - Best Known (113, 113+49, s)-Nets in Base 3

Best Known (113, 113+49, s)-Nets in Base 3

(113, 113+49, 204)-Net over F₃ — Constructive and digital

Digital (113, 162, 204)-net over F₃, using

trace code for nets [i] based on digital (5, 54, 68)-net over F₂₇, using
- net from sequence [i] based on digital (5, 67)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 5 and N(F) ≥ 68, using
    - a function field by SÃ©mirat [i]

(113, 113+49, 360)-Net over F₃ — Digital

Digital (113, 162, 360)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(113, 113+49, 7757)-Net in Base 3 — Upper bound on s

There is no (113, 162, 7758)-net in base 3, because

1 times m-reduction [i] would yield (113, 161, 7758)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 65689 243352 819549 762964 743884 629318 543962 232014 187973 598253 069271 165063 281393 > 3¹⁶¹ [i]