MinT - Best Known (127, 127+93, s)-Nets in Base 3

Best Known (127, 127+93, s)-Nets in Base 3

(127, 127+93, 148)-Net over F₃ — Constructive and digital

Digital (127, 220, 148)-net over F₃, using

trace code for nets [i] based on digital (17, 110, 74)-net over F₉, using
- net from sequence [i] based on digital (17, 73)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
    - a function field by GarcÃa and Quoos [i]

(127, 127+93, 174)-Net over F₃ — Digital

Digital (127, 220, 174)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(127, 127+93, 1636)-Net in Base 3 — Upper bound on s

There is no (127, 220, 1637)-net in base 3, because

1 times m-reduction [i] would yield (127, 219, 1637)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 312 416340 603251 846203 691475 414545 632034 254563 130075 034061 841731 954173 761186 142813 068675 997889 170549 803425 > 3²¹⁹ [i]