MinT - Best Known (120, 120+49, s)-Nets in Base 3

Best Known (120, 120+49, s)-Nets in Base 3

(120, 120+49, 246)-Net over F₃ — Constructive and digital

Digital (120, 169, 246)-net over F₃, using

3¹ times duplication [i] based on digital (119, 168, 246)-net over F₃, using
- trace code for nets [i] based on digital (7, 56, 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]

(120, 120+49, 430)-Net over F₃ — Digital

Digital (120, 169, 430)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(120, 120+49, 10696)-Net in Base 3 — Upper bound on s

There is no (120, 169, 10697)-net in base 3, because

1 times m-reduction [i] would yield (120, 168, 10697)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 143 599951 491323 815355 066293 205561 352015 394476 252787 802341 809823 392893 456444 251617 > 3¹⁶⁸ [i]