MinT - Best Known (120, 120+79, s)-Nets in Base 3

Best Known (120, 120+79, s)-Nets in Base 3

(120, 120+79, 148)-Net over F₃ — Constructive and digital

Digital (120, 199, 148)-net over F₃, using

7 times m-reduction [i] based on digital (120, 206, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 103, 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]

(120, 120+79, 190)-Net over F₃ — Digital

Digital (120, 199, 190)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(120, 120+79, 1997)-Net in Base 3 — Upper bound on s

There is no (120, 199, 1998)-net in base 3, because

1 times m-reduction [i] would yield (120, 198, 1998)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 29824 629180 115228 948505 666749 793782 294435 232047 444806 176494 879789 538538 830578 157834 369464 107449 > 3¹⁹⁸ [i]