MinT - Best Known (122−28, 122, s)-Nets in Base 4

Best Known (122−28, 122, s)-Nets in Base 4

(122−28, 122, 1036)-Net over F₄ — Constructive and digital

Digital (94, 122, 1036)-net over F₄, using

4² times duplication [i] based on digital (92, 120, 1036)-net over F₄, using
- trace code for nets [i] based on digital (2, 30, 259)-net over F₂₅₆, using
  - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(122−28, 122, 1926)-Net over F₄ — Digital

Digital (94, 122, 1926)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(122−28, 122, 355504)-Net in Base 4 — Upper bound on s

There is no (94, 122, 355505)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 28 269633 301376 001299 541853 761197 187609 271052 210751 185019 490226 574962 049736 > 4¹²² [i]