MinT - Best Known (122, 170, s)-Nets in Base 8

Best Known (122, 170, s)-Nets in Base 8

(122, 170, 1026)-Net over F₈ — Constructive and digital

Digital (122, 170, 1026)-net over F₈, using

t-expansion [i] based on digital (114, 170, 1026)-net over F₈, using
- 2 times m-reduction [i] based on digital (114, 172, 1026)-net over F₈, using
  - trace code for nets [i] based on digital (28, 86, 513)-net over F₆₄, using
    - net from sequence [i] based on digital (28, 512)-sequence over F₆₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513, using
        the Hermitian function field over F₆₄ [i]

(122, 170, 4871)-Net over F₈ — Digital

Digital (122, 170, 4871)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(122, 170, 3492611)-Net in Base 8 — Upper bound on s

There is no (122, 170, 3492612)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 3351 969401 957807 720123 252680 104688 649186 601219 091296 309914 189309 814765 701230 655582 438641 151398 346111 874319 791647 407168 917946 650803 583681 807904 196193 717088 > 8¹⁷⁰ [i]